# Two ideal springs oscillating, find amplitude and phase difference between them

1. Jul 24, 2012

### scrodger

Hi, I am repeating first year exams and would really appreciate some help with my study. Just can't seem to get my head around this problem.

1. The problem statement, all variables and given/known data
Consider two identical ideal springs with a mass m attached which are harmonically oscillating out of phase relative to each other, with the spring constant k = 100 N/m and the mass m = 1x10-3 kg.
At the time t0 = +0.1 sec, the displacement of the spring 1 is x1(t0) = 10 mm and the displacement of spring 2 is x2(t0) = 1 mm.
(i) Calculate the value of the amplitude A of each oscillation.
(ii) Calculate the value of the phase-difference ∅ between the two oscillators.

2. Relevant equations
ω = $\sqrt{k/m}$
x = Acos(ωt + ∅)
kA2 = mv2 + kx2

3. The attempt at a solution
So I calculated ω = 316.228 rad/s. In order to find A, I can use either the position equation or the energy equation. But both of these have an unknown variable. I can't seem to figure out how to find one of these. In the case of the equation x = Acos(ωt + ∅), is ∅ included in this as I am given time with the symbol t0? Any help would really be appreciated. Also for part (ii) of the question, I have never solved a question before asking for the phase difference between two objects. Do you just subtract one from the other? Or is there a specific method?
Thanks

2. Jul 24, 2012

### NoPoke

are you sure that there is no extra piece of information? It seems a little odd that the question would give you displacements at time = 0.1sec without telling you something about time = 0.

3. Jul 26, 2012

### scrodger

Yep, I have posted the entire question. Does the subscript 0 on the t mean anything?

4. Jul 26, 2012

### NoPoke

t0 usually means time zero or initial starting time.

so t0 = 0.1sec or t0 = +0.1sec are both a little odd.

I can't see a way of providing values for A and phi without more information